Subgroups — C₁₃×#24157 #15710496

Order 3328.

1114 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2035	C₂	1	2	yes	maximal
6	C₁₃×#2001	C₂	1	2	yes	maximal
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1878	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₁₃×#533	—	2	4	no	—
14	C₁₃×#533	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₂×C₁₃×#117	—	2	1	no	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#475	—	2	4	no	—
27	C₁₃×#462	—	2	4	no	—
28	C₂×C₁₃×#106	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	2	yes	—
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×#103	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#387	—	2	1	no	—
39	C₁₃×#385	—	2	1	no	—
40	C₁₃×#380	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#340	C₂²	1	2	yes	—
46	C₁₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×Q₁₆	—	2	4	no	—
54	C₂×C₁₃×Q₁₆	—	2	4	no	—
55	C₂×C₁₃×Q₁₆	—	4	2	no	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
61	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
62	C₁₃×#125	—	2	8	no	—
63	C₁₃×C₂²⋊Q₈	—	2	8	no	—
64	C₁₃×C₂²⋊Q₈	—	2	4	no	—
65	C₁₃×C₂²⋊Q₈	—	2	2	no	—
66	C₁₃×C₂²⋊Q₈	—	2	4	no	—
67	C₁₃×C₂²⋊Q₈	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	8	no	—
69	C₄×Q₈×C₁₃	—	2	4	no	—
70	C₄×Q₈×C₁₃	—	2	4	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	—	2	2	no	—
73	C₁₃×#117	—	2	8	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₁₃	—	2	2	no	—
90	C₂×C₄²×C₁₃	—	2	2	no	—
91	C₂×C₄²×C₁₃	—	2	2	no	—
92	C₂×C₄²×C₁₃	—	2	1	no	—
93	C₂×C₄²×C₁₃	—	2	1	no	—
94	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#106	—	2	4	no	—
99	C₁₃×C₄⋊C₈	—	2	2	no	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×#103	—	2	4	no	—
102	C₁₃×#103	—	2	4	no	—
103	C₁₃×#103	—	2	4	no	—
104	C₁₃×#103	—	4	2	no	—
105	C₁₃×C₂²⋊C₈	—	4	2	no	—
106	C₁₃×#95	—	2	1	no	—
107	C₁₃×#95	—	2	1	no	—
108	C₁₃×#95	—	2	1	no	—
109	C₁₃×#95	—	2	1	no	—
110	C₁₃×#95	—	2	1	no	—
111	#24157	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	2	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	4	2	no	—
125	C₂×Q₈×C₁₃	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
127	C₂×Q₈×C₁₃	#41	1	2	yes	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×Q₁₆	—	4	8	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	4	2	no	—
172	C₁₃×C₄⋊C₄	—	4	2	no	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
174	C₁₃×C₄⋊C₄	#41	1	2	yes	—
175	C₁₃×C₂²⋊C₄	—	2	8	no	—
176	C₁₃×C₂²⋊C₄	—	2	4	no	—
177	C₁₃×C₂²⋊C₄	—	4	2	no	—
178	C₄²×C₁₃	—	2	8	no	—
179	C₄²×C₁₃	—	2	2	no	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	4	2	no	—
184	C₄²×C₁₃	—	4	2	no	—
185	C₄²×C₁₃	C₂×D₄	1	2	yes	—
186	C₄²×C₁₃	C₂×D₄	1	2	yes	—
187	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
188	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
191	#2035	C₂×C₁₃	1	2	yes	—
192	#2001	C₂×C₁₃	1	2	yes	—
193	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#1878	C₂×C₁₃	1	2	yes	complemented
196	#1865	C₂×C₁₃	1	2	yes	complemented
197	#1797	C₂×C₁₃	1	1	yes	characteristic
198	C₂³×C₁₃	—	2	1	no	—
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	—	2	1	no	—
203	C₂³×C₁₃	—	2	1	no	—
204	C₂³×C₁₃	#137	1	2	yes	—
205	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₁₃	—	2	2	no	—
207	Q₈×C₁₃	—	2	4	no	—
208	Q₈×C₁₃	—	2	4	no	—
209	Q₈×C₁₃	—	2	2	no	—
210	Q₈×C₁₃	—	4	1	no	—
211	Q₈×C₁₃	—	4	2	no	—
212	Q₈×C₁₃	—	4	2	no	—
213	Q₈×C₁₃	—	4	1	no	—
214	Q₈×C₁₃	—	4	8	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	#120	1	2	yes	—
250	C₂×C₄×C₁₃	#120	1	2	yes	—
251	C₂×C₄×C₁₃	#135	1	2	yes	—
252	C₂×C₄×C₁₃	#137	1	2	yes	—
253	C₂×C₄×C₁₃	#137	1	2	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
260	C₈×C₁₃	—	4	2	no	—
261	C₈×C₁₃	—	4	2	no	—
262	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
263	#533	—	2	4	no	—
264	#533	—	2	4	no	—
265	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#125	—	2	1	no	—
268	C₂×C₂²⋊Q₈	—	2	1	no	—
269	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
270	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄×Q₈	—	2	1	no	—
272	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
274	C₂×#117	—	2	1	no	—
275	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
276	#475	—	2	4	no	—
277	#462	—	2	4	no	—
278	C₂×#106	C₂²×C₁₃	1	2	yes	—
279	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#103	C₂²×C₁₃	1	2	yes	—
282	C₂×#103	C₂²×C₁₃	1	2	yes	—
283	C₂×#103	C₂²×C₁₃	1	2	yes	—
284	C₂×#103	C₂²×C₁₃	1	2	yes	—
285	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
286	#391	C₂²×C₁₃	1	1	yes	characteristic
287	#389	C₂²×C₁₃	1	1	yes	characteristic
288	#387	—	2	1	no	—
289	#385	—	2	1	no	—
290	#380	C₂²×C₁₃	1	1	yes	characteristic
291	C₄×C₄⋊C₄	—	2	1	no	—
292	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
293	C₄×C₂²⋊C₄	—	2	1	no	—
294	#340	C₂²×C₁₃	1	2	yes	—
295	#340	C₂²×C₁₃	1	2	yes	—
296	#336	C₂²×C₁₃	1	2	yes	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	—	4	1	no	—
303	C₂²×C₁₃	—	4	1	no	—
304	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
305	C₂²×C₁₃	#525	1	1	yes	characteristic
306	C₂²×C₁₃	#537	1	1	yes	characteristic
307	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
308	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
309	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
310	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	—	4	1	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	1	no	—
318	C₄×C₁₃	—	4	4	no	—
319	C₄×C₁₃	—	8	1	no	—
320	C₄×C₁₃	—	8	1	no	—
321	C₄×C₁₃	#452	1	4	yes	—
322	C₄×C₁₃	#546	1	1	yes	characteristic
323	C₄×C₁₃	#547	1	1	yes	characteristic
324	C₄×C₁₃	#548	1	1	yes	characteristic
325	C₄×C₁₃	#550	1	1	yes	characteristic
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
328	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×Q₁₆	—	2	4	no	—
333	C₂×Q₁₆	—	2	4	no	—
334	C₂×Q₁₆	—	4	2	no	—
335	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
336	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
340	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
341	#125	—	2	8	no	—
342	C₂²⋊Q₈	—	2	8	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	8	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	—	2	4	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	#117	—	2	8	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₄²	—	2	2	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	#106	—	2	4	no	—
378	C₄⋊C₈	—	2	2	no	—
379	C₄⋊C₈	—	2	2	no	—
380	#103	—	2	4	no	—
381	#103	—	2	4	no	—
382	#103	—	2	4	no	—
383	#103	—	4	2	no	—
384	C₂²⋊C₈	—	4	2	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	C₂×C₁₃	—	4	2	no	—
391	C₂×C₁₃	#2407	1	1	yes	characteristic
392	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
393	C₂×C₁₃	#3004	1	1	yes	characteristic
394	C₂×C₁₃	#3107	1	1	yes	characteristic
395	C₂×C₁₃	#3113	1	1	yes	characteristic
396	C₂×C₁₃	#3248	1	1	yes	characteristic
397	C₂×C₁₃	#3255	1	1	yes	characteristic
398	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
413	C₂×Q₈	C₁₃×#41	1	2	yes	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
438	Q₁₆	—	4	8	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
460	C₄⋊C₄	C₁₃×#41	1	2	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₄²	—	2	8	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	4	2	no	—
470	C₄²	—	4	2	no	—
471	C₄²	C₂×D₄×C₁₃	1	2	yes	—
472	C₄²	C₂×D₄×C₁₃	1	2	yes	—
473	C₁₃	#24157	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	C₁₃×#137	1	2	yes	—
481	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
482	Q₈	—	2	2	no	—
483	Q₈	—	2	4	no	—
484	Q₈	—	2	4	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	4	8	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	1	no	—
491	C₂×C₄	—	2	8	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	C₁₃×#120	1	2	yes	—
526	C₂×C₄	C₁₃×#120	1	2	yes	—
527	C₂×C₄	C₁₃×#135	1	2	yes	—
528	C₂×C₄	C₁₃×#137	1	2	yes	—
529	C₂×C₄	C₁₃×#137	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
533	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
534	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
536	C₈	—	4	2	no	—
537	C₈	—	4	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
546	C₂²	C₁₃×#525	1	1	yes	characteristic
547	C₂²	C₁₃×#537	1	1	yes	characteristic
548	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
549	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
550	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
551	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	4	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	4	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	C₁₃×#452	1	4	yes	—
563	C₄	C₁₃×#546	1	1	yes	characteristic
564	C₄	C₁₃×#547	1	1	yes	characteristic
565	C₄	C₁₃×#548	1	1	yes	characteristic
566	C₄	C₁₃×#550	1	1	yes	characteristic
567	C₂	—	4	2	no	—
568	C₂	C₁₃×#2407	1	1	yes	characteristic
569	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
570	C₂	C₁₃×#3004	1	1	yes	characteristic
571	C₂	C₁₃×#3107	1	1	yes	characteristic
572	C₂	C₁₃×#3113	1	1	yes	characteristic
573	C₂	C₁₃×#3248	1	1	yes	characteristic
574	C₂	C₁₃×#3255	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₃×#475	C₂	semidirect
3. C₂×C₁₃×#462	C₂	semidirect
7. C₁₃×#1988	C₂	semidirect
8. C₁₃×#1981	C₂	semidirect
9. C₁₃×#1878	C₂	semidirect
10. C₁₃×#1865	C₂	semidirect
111. #24157	C₁₃	direct (N × H)
188. C₂×#475	C₂×C₁₃	semidirect
189. C₂×#462	C₂×C₁₃	semidirect
193. #1988	C₂×C₁₃	semidirect
194. #1981	C₂×C₁₃	semidirect
195. #1878	C₂×C₁₃	semidirect
196. #1865	C₂×C₁₃	semidirect
473. C₁₃	#24157	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#533	2
C₂×C₁₃×#475	2
C₂×C₁₃×#462	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2035	2
C₁₃×#2001	2
C₁₃×#1988	2
C₁₃×#1981	2
C₁₃×#1878	2
C₁₃×#1865	2
C₁₃×#1797	2
#24157	13

Subgroups — C13×#24157 #15710496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24157 #15710496